In order to enable optical fibers to be connected together in electrical contact devices for instance, it is necessary to center the fibers accurately in relation to one another. To this end, are used ferrules which are connected to the ends of respective fibers and used as fiber centering guides, since the fiber ends cannot themselves be used for this purpose. The ferrules are provided with a central hole into which the optical fiber is inserted and then glued or welded into firm contact with the ferrules, whereafter the outwardly protruding fiber end and the end of the ferrule are ground and polished to a flat surface. The drawback with this method is that the task of securing the ferrule on the end of the fiber is both work-demanding and time-consuming.